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Re: ZFC and God
Posted:
Jan 28, 2013 3:24 PM
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On 28 Jan., 20:37, Virgil <vir...@ligriv.com> wrote:
> In article
> <28f8bc0b-7217-4f75-9fc0-22b3d9f2c...@u16g2000yqb.googlegroups.com>,
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> WM <mueck...@rz.fh-augsburg.de> wrote:
> > On 27 Jan., 23:27, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
>
> > > >> it follows *FROM THE AGREED DEFINITION* that 0.777... has no
> > > >> terminating decimal representation.
>
> > > > Show that in your 0.777..., and in particular in the anti-diagonal of
> > > > a list of terminating decimals, there is an index k that does not
> > > > belong to a FISON {1, 2, ..., n}.
>
> > > Utterly irrelevant to the matter at hand. Evidently, you don't
> > > understand the definition you agreed to.
>
> > Please let me know where I agreed to that definition.
> > Of course, when working in the terminating decimals, every anti-
> > diagonal is terminating.
>
> But WM is the only one limiting himself so foolishly.
>
> The rest of us realize that truly infinite series are required in real
> analysis so refuse to handicap ourselves unnecessarily.
I am not discussing what is required. A mathematician should be
interested and able in working on a special problem. This problem I
have stated: We use the domain of all terminating decimals. (That
means we have no infinite decimal. But we have on the other hand no
largest index.) From a list of all these terminating decimals we
construct an anti-diagonal. By construction it takes every digit from
an entry of the list and switches it to another value - but that is
not important for the fact that every digit of the diagonal belongs to
a terminating sequence. Hence there is for every digit some k as
required by Jesse.
And we can prove by induction that we never leave the domain of
terminating decimals. What this may be good for, is another question.
But I can answer it: Everything in analysis that is based upon digits
belongs to this domain. It is simply impossible to leave it unless ypu
define - by a finite definition - that you want to deal with infinite
sequences of digits.
And you know how many finite definitions are available, I presume.
Regards, WM
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